5 20
Journal of the American Chemical Society
/ I02:2 / January 16, 1980
A Study of Proton Relaxation Mechanisms, Stereochemistry, and Dynamics of the Decapeptide Tyrocidine A Mei-chang Kuo, Torbjorn Drakenberg, and William A. Gibbons* Contributionfrom the Department of Biochemistry, College of Agriculture and L$e Sciences, The University of Wisconsin, Madison, Wisconsin 53706. Received January 12, 1979
Abstract: Correlation times and interproton distances for the backbone of the peptide tyrocidine A, an acalogue of gramicidin S, have been determined from proton spin-lattice relaxation rate measurements in the monoselective, Ri(i),biselective, Ri(?,j), and nonselective, R'(NS), modes. The values obtained agree with those determined from NOE measurements. These relaxation parameters were also calculated for some protons from the correlation time and the interproton distances of the tyrocidine A molecule assuming the latter tq contain @I-turn,@II'-turn, and antiparallel @-pleated sheet moieties. In every case the calculated relaxation parameters, Ri(i) and R i ( N S ) ,agreed with the experimental values.
Introduction Although proton relaxation studies of peptides have been reported,' quantitation in terms of distance, conformation, and correlation times was unsatisfactory due to neglect of crossrelaxation effects.2 The latter have been treated for small molecule^^-^ and evaluated in amino acid^^,^ and from a combination of NOES and monoselective spin-lattice relaxation times. Cross-relaxation effects in proteins have been recognized but not evaluated quantitatively. The cross-relaxation rates, ai,, have been measured for gramicidin S7-9and tyrocidine AI3 via the NOE and used to estimate their interproton distances and correlation times. Here we report a proton relaxation study of tyrocidine A; the r+ r$, and transannular interproton distances were evaluated and are consistent with the type I@-turn,type II'P-turn, and antiparallel @-pleated sheet c ~ n f o r m a t i o n l previously ~-~~ reported. This confirms the conclusion regarding conformation in the NOE study,I3 demonstrates the additivity of spin-lattice relaxation parameters, and proves that all relaxation rates are dominated by dipolar mechanisms principally involving protons but also I4N nuclei. Experimental Section The tyrocidine A was obtained from Professor Lyman C. Craig and had been purified by counter current distribution. The samples were prepared by dissolving 4.5 mg of tyrocidine A in 1 m L of 100% Me2SO-ds and were thoroughly deoxygenated. The NMR spectra were taken on a Bruker WH 270 spectrometer equipped with a Nicolet I I 8 0 computer. (T-180'-~-90'-),, pulse sequences were used in the T I experiments. The nonselective 180' pulse was typically 20 ps, and 200 FIDs were accumulated; the selective 180' pulse, provided by the decoupler channel, was typically 10 ms and 64 FIDs were accumulated. In the biselective experiments the decoupler frequency was modulated to produce two sidebands which simultaneously inverted the two proton resonances to be studied. The relaxation rates were determined from semilogarithmic plots of log ( l o - 12)vs. delay time T. Typically, T values of up to 200 ms were used. Examples of spectra used to determine monoselective, biselective, and nonselective proton spin-lattice relaxation rates are shown in Figures 1, 2, and 3, respectively. The temperature was kept a t 26 f 1 "C by the Bruker temperature control unit and was calibrated with the methanol and ethylene glycol standard samples.
Error Analysis 1. Reproducibility. Some of the selective relaxation rates have been determined from up to four different experiments, showing a total spread of less than 10%.This indicates that a single measurement can be reproduced to within f 5 % of the mean value. 0002-7863/80/ 1502-0520$01 .OO/O
2. Systematic Errors. Systematic errors due to imperfect rf pulses and nonresonance conditions have been discussedI6 and are here assumed to be unimportant; furthermore, if they are always the same, they will cancel in the calculation of crossrelaxation rates and distances. A more serious source of error may be introduced in the determination of the relaxation rates from the semilogarithmic plots, which assumes that the initial slope approximation is valid for the whole range of T values used. When there is cross relaxation among the protons relaxing each other the recovery of the magnetization after the 180' pulse is never purely exponential in the selective experiment and, in the nonselective experiment, the recovery is exponential only when the relaxation rates are the same for all protons relaxing the studied one.2 We have performed some test calculations, where cross-relaxation effects were taken into account for AX and AX2 systems. These calculations show that under our conditions the selective relaxation rates abtained from the semilogarithmic plots are in error by 5 1 0 % due to the neglect of cross-relaxation effects. The experimental relaxation rates are always slower than the true ones. For the nonselective relaxation rates the situation is more complex and the errors can be appreciable, and in either direction, depending on how much the relaxation rateof the studied proton deviates from that of the proton(s) causing the relaxation. Ha5and Ha9 represent the most unfavorable cases for the present molecule because each a proton is mainly relaxed by its fl protons; however, the error was never more than 15% even though the relaxation rate of the protons was four times that of the a proton. In this case the experimental value proved to be faster than the true one. A combination of the most unfavorable cases for the selective and nonselective relaxation rates can result in an error of as much as 25% in the determined u values; this, however, gives only a 4% error in the distance derived from a. Since the errors are systematic the calculated correlation times are probably underestimated by up t o 25%. M o r e a c c u r a t e values have to await a more rigorous treatment of the recovery curves, which is now in progress. Results and Discussion The sequence of tyrocidine A and the proposed conformation are shown in Figure 4. 1. Proton Microenvironment from Spin-Lattice Relaxation Rates. The monoselective spin-lattice relaxation rate is deby R'(I)= 2 w ,
+ w,+ wo
(1)
where Wo, W l , and W2 are the transition probabilities for the 0 1980 American Chemical Society
Kuo, Drakenberg. Gibbons
1 Decapeptide
52 1
Tyrocidine A
Table I. Relaxation Parameters for Backbone Protons of Tyrocidine Aa
R (N S),
~
~
R'(7),
S-I
S-I
2.2 2.7 2.4 2.9 2.4 2.5 0.9 2.3 1 .o
3.4 4.0 3.6 4.1 3.4 4.0 1.6 4.0 1.8
.I8 .I6
~~
Temperature, 26 " C ;concentration, 15 mg/mL of MeZSO-ds.
zero, one, and two quantum transitions, respectively. R i ( i )is sometimes said not to include cross-relaxation however, the-recovery of the magnetization after a 180' pulse does and Ri(i)can only be obtained, using the semilogarithmic plot, from the initial slope of the recovery curve (see Error Analysis). One approach to evaluating the microenvironments of protons is through the measurement of monoselective spinlattice relaxation rates. The data for backbone protons in Table I obtained by experiments such as those shown in Figure 1 reveals that R i ( i )varies from 1.6 to 4.7 s-l and can be discussed with reference to the conformation of tyrocidine A deduced from scalar coupling constants,15 N O E ratios,13 cross-relaxation parameters,I3 u ratios,I3 and hydrogenbonding studies.15 This conformation, shown in Figure 4, contains type I P-turn, type II'p-turn, and antiparallel @pleated sheet conformational moieties. The relaxation rates, Ri(T),of the a protons of Gln9 and Pro5, 1.8 and 1.6 s-l, respectively, reflect the relative lack of protons within a 4-A radius (the microenvironment). The 4.0-s-l rate for O r n 2 H a is readily accounted for by efficient relaxation by NH(2), NH(3), H a ( 7 ) , and NH(8) as well as the Om2side-chain protons. An equally rich and similar proton microenvironment accounts for the efficient H a ( 7 ) relaxation. Each amide proton, NH(i), is relaxed primarily by the H a ( i ) and H a ( i - I), by the /3 protons of the ith and ( i - 1)th residues, and by transannular protons similar to the H a ( 2 ) H a ( 7 ) effects discovered by N O E difference spectroscopy.Is In general we can write the following additivity relationship for an a or amide proton:
R'(i) = R ,
+ R+ + R , + Ro + RTA
where R , is the interaction between the a and NH protons in the same residue, R+is the interaction between NH(i) and a(i - 1) protons, R, is the interaction between an a or N H proton and the side-chain protons, RTAis the transannular interaction, and Ro is the relaxation rate due to mechanisms other than proton-proton dipolar relaxation. For a rigid backbone terms R, and R+ will depend only on the correlation time for the overall motion of the molecule and on the distances r$ or ' 6 , respectively. The term R, may or may not be dependent on internal motion of the side chain in addition to distance and overall motion. RTAcan, as well as R,, be the sum of several terms; see, for example, H a ( 7 ) in Table V. The only contribution from other mechanisms that has to be taken into account here is the dipolar relaxation from 14N on protons directly bound to the nitrogen, R N H= 1.4 s-I. Contributions from other mechanisms can safely be assumed to be less than 0.1 s-1. 2. Correlation Times from Cross-Relaxation Rates. As previously shown7 u for a pair of protons can be indirectly
9
0
7 P P M
6
5
4
(HMS)
Figure 1. Monoselective proton spin-lattice relaxation rate measurements of the Gln9 01 proton (1) of tyrocidine A. The 4-9-ppm region of the NMR spectrum is shown (top). All relaxation spectra were recorded with a selective ( 1 80-~-90-T), pulse sequence. To obtain difference relaxation spectra, the relaxation spectrum for each T value was subtracted from the T = = spectrum. In this manner the individual 7 difference relaxation spectra showed only that proton which was excited by the selective 180° pulse.
calculated from the product of NOEs and R i ( i )values or directly from the following equation^:^ Ri(i,J)- Ri(7) = (2)
RjG,;) - RjG) =
(3)
where Ri(?,j)is the biselective relaxation rate obtained when resonances i and j are inverted simultaneously and ai, = Wzij - Woij,the cross-relaxation rate. These relaxation rates and the calculated u's are shown in Tables I and 11, respectively. The biselective relaxation rates of protons i and j were measured as previously described;6 a typical example is shown in Figure 2. The u's calculated from eq 2 and 3 and those from the NOEs13 are shown in Table 11. The close resemblance of ai, and u,i calculated from NOEs and relaxation rates for the N H - H a moieties of Orn2 and Gln9 demonstrates the accuracy of both experiments; furthermore, u values for other pairs of protons in tyrocidine A, where measurable by several methods, always agreed (with one exception, Table IV). Correlation times and/or distances for interproton vectors corresponding to a0 values were calculated2 from the equation
+
a,, = ( y ~ ~ t t ~ ) ( l / r i , ~ ) 1 3 7 ~ '2, 0/ (050 ~ 7 , ~-) ~ ~ ~ j / l O ) (4)
where y is the proton gyromagnetic ratio, h is Planck's constant, ry is the interproton distance, ~~~j is the correlation time for the motion of the vector connecting protons i a n d j , and 00 is the spectrometer frequency. (a)The correlation times for 6vectors of residues 2 , 3 , 4 , 9 , and 10 calculated from relaxation measurements and N O E / relaxation measurements are shown in Table 11, columns 4 and 6, respectively. In the case of Orn2 the four calculated correlation times, 1.24, 1.62, 1.48, and 1.42 X s, are, within experimental error, in agreement with each other and with the 7,values for all C$ interproton vectors of other residues. Considering the differences in 3 J N H H a values, and hence r , dis-
522
Journal of the American Chemical Society
9
8
6
7
P
P
M
5
/ 102.2 / January 16, 1980
4
(HMS)
Figure 2. Biselective proton spin-lattice relaxation rate measurements: the Gln9 cy (1) and Gln9 amide protons (1) were simultaneously excited with the selective 180° pulse and the nonselective 90° pulse was applied at different time intervals T . Incomplete cancellation of the very intense aromatic ring protons can be seen in the difference relaxation spectra around 7 . 3 ppm.
T Y P E 11’ H, H
c4,; H-N
4
/N-C C
Yl
0
hc = o
\ H-C
c” o=c
dC h dN
Figure 3. Nonselective proton spin-lattice relaxation rate measurements of tyrocidine A.
Figure 4. Proposed structure of tyrocidine A.
tances, and the uncertainties in the relaxation rates, this agreement is satisfactory and gives an average correlation time for the molecule of 1.3 X s. The H61-H62, HPl-HP2, and H6-Hc distances of residues ProS, Am8, and Tyr’O are independent of motion or conformation and when inserted in eq 4, using the u values of Table II,giveT,= 1.10(1.19), 1.38(1.41),and 1.16(1.30) X
s, respectively; the values in parentheses are NOE-derived correlation times.13 (b) Interproton Distances. The T,, taken as the mean from Table 11, and spin-lattice relaxation parameters, Tables I1 and 111, for ProsH61-Pro5H62 was used to calculate all r#’s for residues 2, 3,4,9, and 10 and, as expected, the distances agree, Table IV, with those from 3 J N H H a and the Karplus curve. This,
Kuo, Drakenberg, Gibbons
523
Decapeptide Tyrocidine A
Table 11. Correlation Times for Proton-Proton Vectors of Tyrocidine A R'(7) + ~
H( i)-H (j) NH(2)-Ha(2) H a(2) -N H (2) NH(3)-Ha(3) NH(4)-Ha(4) N H (9) - H a ( 9) Ha( 9)-N H (9) NH(IO)-Ha(10) Hbl(5)-H62( 5) HPl(g)-HP2(8) HE(1 0) -Ha( 10) Ha( 1 0 ) - H ~ (10)
S-I
3.33 3 .go 3.98 3.50 4.57 1.70 3.35 3.70 4.18 1 .oo
i j ,
Uij,
rij,
rcij
S-1
A
(x109), s c
2.95" 2.95" 2.94" 2.83" 2.86" 2.86" 2.96" 1.776 1.776 2.44b 2.44b
1.24 1.62 1.25 1.30
-0.07 -0.1, -0.0s -0.10 -0.0~ -0.10 -0.0s -1.11
-1.89 -0.20
(ui,/Ri(7))X Ri(T), S-1
rcii
(x109), ~d 1.48 1.41 1.19 1.36 1.28 1.40 1.i6 1.1~ 1.41 1.25 1.34
-0.10 -0.0~ -0.07 -0.11 -0.0~ -0.11 -0.0~ - 1.42 -1.95
1.19
1.33 1.32 1.10
1.38
-O& -0.2~
1.16
" Interproton distances estimated from 3 J ~ values.13 ~ ~ , Interproton distances calculated from standard bond angle and bond distance.21 Correlation times calculated from u values obtained by purely relaxation rate measurements. Correlation times calculated from a combination of NOEs and monoselective relaxation rates. Table 111. Spin-Lattice Relaxation Parameters of the Side-Chain
Table IV. Interproton Distances Calculated from Cross-Relaxation
Protons
Parameters"
2.4 2.9 2.9 0.9 0.8
3.9 4.8 6.1 1.5 1.2
in certain circumstances, provides a method of removing part of the fourfold C$ degeneracy obtained from 3 J ~ H H a values. l 9 The r+ distances for residues 8 and 2, Table IV, calculated from the two a values between N H ( 9 ) - H a ( 8 ) and NH(3)H a ( 2 ) , are equal (2.6 and 2.1 A) and the same as those derived from the NOE.I3 The Ha(4)-H61(5) distance, 2.2 A, is equal to that derived from NOE ratiosI3 and to the corresponding distance of gramicidin S7,8(Table IV). The interproton distance between NH(9) and the protons of residue 8 provide the only case where the disagreement between distances derived here and those previously derived13 is more than 0.2 A. 3. Calculation of Ri(NS) and R i ( a Values. If (a) the conclusion that the relaxation of Ha's in tyrocidine A are fully explained by dipolar mechanisms is correct, (b) the backbone correlation time is 7c = 1.3 X s, and (c) if all 4, #, and transannular distances are those of the turns and antitarallel P-pleated sheet, we can calculate R i ( N S ) and Ri(i) and compare them with the experimental values. This comparison is shown in Table V. If a n additivity relationship holds, both the observed and calculated R'(NS) and R'(i)values should agree, respectively; this would be additional evidence that the proton relaxation mechanisms are fully dipolar. W e can write2
where the meaning of the parameters is the same as in eq 4. Assuming only one 7 c i j exists, all the distances, rij, between H a ( 7 ) and each of the protons NH(7), NH(8), H a ( 2 ) , NH(3), HP1(7), and H@2(7)were used in the Z l/rij6 term of eq 5. The calculated Ri($ 3.5 s-l, agrees with the observed value, 4.0, especially considering that the effect of one proton, H6(7), was not accounted for. The distance between H6(7) and H a ( 7 ) depends on the X I and x 2 torsion angles of the D-Phe7
Ha(2)-NH(3) N H (3)-Ha( 2) Ha(2)-Ha(7) Ha(7)-Ha(2) Ha(7)-NH(7,8) H61(5)-Ha(4) NH(9)-Ha(8) NH(9)-HP1(8) H P 1(8)-NH( 9) NH(9)-HP2(8)
3.42 3.46 3.64 3.64 3.34 4.24 4.47 4.07 5.40 4.38
-0.60 -0.49 -0.2~ -0.2~ -0.64 -0.46 -0.13 -0.5s
-0.7s -0.0~
2.12 2.19 2.44 2.41 2.22 2.14 2.13 2.0~ 3.10
a The latter was derived from relaxationb and from NOECexperiments. Interproton distances calculated from u values obtained by purely relaxation rate measurements. Correlation times calculated from a combination of NOEs and monoselective relaxation rates.
residue. Since ~ ' ( 7 = ) +60° and x2(7) = 90 f 30°, this distance can range between 2.5 and 3.6 A. Adding this contribution makes the selective relaxation rate of H a ( 7 ) equal to 3.8 f 0.2 s-l. The nonselective relaxation rate, RHa(')(NS), is the sum of Ri(i)and Zai,. From eq 4, Zaij can be calculated, and therefore the RH4')(NS) (Table V). In a similar way the selective and nonselective relaxation rates of NH(4) and H a ( 5 ) were calculated. For N H ( 4 ) the contributions for HP(3), Hy(3), and H6(3) were ignored, and for H a ( 5 ) the contributions from Hy(5) and H6(5) were also ignored. The results also agree with the observed values. Unfortunately, enough data were not available to do this for other protons, but these examples suffice to illustrate the principle and that the mechanisms are dipolar.
Conclusions In this report we measured the nonselective, R i ( N S ) , biselective, R i ( i , j ) , and monoselective, R i ( i ) ,spin-lattice relaxation rates for tyrocidine A to obtain the cross-relaxation rates, ai,. The latter agreed with a's calculated from N O E meas u r e m e n t ~ . Correlation '~ times for N H , Ha, and side-chain protons, calculated from ai, parameters, agree with those measured previously in NOE studies.' The correlation times for H6-He, H61-H62, and HPl-HP2 vectors of three side chains were, within experimental error, the same as the correlation time for the backbone protons; the latter was in satisfactory agreement with the correlation'time for the backbone of gramicidin S (an analogue) calculated from I3C TI data.2o
5 24
Journal of the American Chemical Society
/
102:2
/ January 16, 1980
Table V. Data Used to Calculate the Monoselective and Nonselective Relaxation Rates of Protons, i , in Tyrocidine A relaxation rates Ri(NS) calcd obsd calcd obsd
R'(ij
HO') H(i)
Ha(7)
NH(8)
NH(7)
Ha(2)
NH(3)
Hpl(7)
HP2(7)
2.1 1.6
3.0 0.2
2.4 0.7
3.1 0.2
3.0 0.2
2.4 0.7
Hcu(3) 2.3 1 .o
Ha(4) 2.8 0.3
Hpl(4) 2.4c 0.7
HP2(4) 2.5c 0.5
14N 1.02 1.4
HflI(5) 2.8 0.3
Hfl2(5) 2.3 0.8
NH(6) 3.0 0.2
ri,,
R,s-l NH(4)
ri,, A a
R , s-1 Ha(5)
ri,,
R,s-I
b
3.6
4.0
2.1
2.3
3.9
3.6
2.9
2.4
1.3
1.6
0.8
0.9
a These distances are between H(i) and all the HG) protons in its microenvironment. It is assumed that the conformation of tyrocidine A is known.13-15 The spin-lattice relaxation rate contributions of H(j) to the relaxation of H(i) calculated from ri,. Mean distances calculated by assuming rotamer populations of 0.68, 0.26, and 0.06 for X I = 180, +60, and -60", respectively.14
The r# distances calculated from u4 values of the Pro5 H61-H62 vector agree with those from 3 J ~measurements ~ c ~ and present a method of removing the 4 angle degeneracy of Karplus curves; they agree also with r# values from N O E measurements. The r+ and transannular distances support the type I@-turnltype II'@-turnlantiparallel @-pleated sheet conformation. The transannular distances prove that the hydrogen bonds exist and provide a method of delineating donor and acceptor groups. The calculated H a - H P and N H - H P distances for certain side chains agree with the side-chain conformations determined from scalar coupling constants and proton-chromophore distance measurement^.'^ The selective spin-lattice relaxation rate, Ri(T), was calculated for one amide and two a protons based upon the measured/known distances from each proton in their microenvironment (
